R for Art Sundays
Strange Attractors: General 2D Map - Part 1
An R experiment to create images generated by the trajectory of a particle according to a strange attractor.
Made with Rcpp, tidyverse
Blog post explaining the experiment: Rcpp, Camarón de la Isla and the Beauty of Maths
Inspired by: Strange Attractors: Creating Patterns in Chaos, by Julien C. Sprott
library(Rcpp)
library(tidyverse)
opt <- theme(legend.position = "none",
panel.background = element_rect(fill="white", color="black"),
plot.background = element_rect(fill="white"),
axis.ticks = element_blank(),
panel.grid = element_blank(),
axis.title = element_blank(),
axis.text = element_blank())
cppFunction('DataFrame createTrajectory(int n, double x0, double y0,
double a1, double a2, double a3, double a4, double a5,
double a6, double a7, double a8, double a9, double a10,
double a11, double a12, double a13, double a14) {
// create the columns
NumericVector x(n);
NumericVector y(n);
x[0]=x0;
y[0]=y0;
for(int i = 1; i < n; ++i) {
x[i] = a1+a2*x[i-1]+ a3*y[i-1]+ a4*pow(fabs(x[i-1]), a5)+ a6*pow(fabs(y[i-1]), a7);
y[i] = a8+a9*x[i-1]+ a10*y[i-1]+ a11*pow(fabs(x[i-1]), a12)+ a13*pow(fabs(y[i-1]), a14);
}
// return a new data frame
return DataFrame::create(_["x"]= x, _["y"]= y);
}
')
a1 <- -0.2826
a2 <- -0.836
a3 <- -0.5587
a4 <- 0.7345
a5 <- -0.345
a6 <- 0.7881
a7 <- -0.4001
a8 <- -1.0978
a9 <- 1.0396
a10 <- -0.28260
a11 <- -0.28261
a12 <- -0.28262
a13 <- -0.28263
a14 <- -0.28264
df <- createTrajectory(10000000, 1, 1, a1, a2, a3, a4, a5, a6,
a7, a8, a9, a10, a11, a12, a13, a14)
mx <- quantile(df$x, probs = 0.05)
Mx <- quantile(df$x, probs = 0.95)
my <- quantile(df$y, probs = 0.05)
My <- quantile(df$y, probs = 0.95)
df %>% filter(x > mx, x < Mx, y > my, y < My) -> df
plot <- ggplot(df) +
geom_point(aes(x, y), shape=46, alpha=0.01, size=0, color="black") +
scale_x_continuous(expand = c(0,0))+
scale_y_continuous(expand = c(0,0))+
coord_fixed() +
opt
plot